Absolute exponential stability criteria of delay time-varying systems with sector-bounded nonlinearity: a comparison approach

TL;DR

This paper develops new criteria for ensuring the absolute exponential stability of delay time-varying systems with sector-bounded nonlinearities, extending previous results and applicable to both continuous and discrete systems.

Contribution

It introduces novel stability criteria using comparison principles and positive system properties, covering and extending existing results in the field.

Findings

New stability criteria for delay time-varying systems with sector-bounded nonlinearities.

Criteria applicable to both continuous-time and discrete-time systems.

Illustrative examples demonstrating the effectiveness of the criteria.

Abstract

Absolute exponential stability problem of delay time-varying systems (DTVS) with sector-bounded nonlinearity is presented in this paper. By using the comparison principle and properties of positive systems we derive several novel criteria of absolute exponential stability, for both continuous-time and discrete-time nonlinear DTVS. When applied to the time-invariant case, the obtained stability criteria are shown to cover and extend some previously known results, including, in particular, the result due to S.K. Persidskii in Ukrainian Mathematical Journal, vol. 57(2005). The theoretical results are illustrated by examples that can not be treated by the existing ones.